Hybrid uncertainty model for multi-state systems and linear programming-based approximations for reliability assessment

Abstract

This article studies reliability assessment for Multi-State Systems (MSSs) with components states that are uncertain in both probability and performance realizations. First, we propose a model of (discrete) Hybrid Uncertainty Variable (HUV) for modeling the hybrid uncertainty of the MSS, in which both state performance levels and associated probability level are described by uncertain values. The HUV can be regarded as a generalization of random variable whose realizations and corresponding probabilities are both uncertain values. Especially the uncertain probabilities are controlled by the probability law. Leveraging the HUV-based hybrid uncertainty model, the primitive probability law is considered throughout the whole process from modeling component state probabilities, through the resulting system state probabilities, to the final reliability computations. Therefore, the information loss is reduced to a minimum. Furthermore, we develop a framework for assessing the reliability of the MSS with hybrid uncertainty. In particular, due to hybrid uncertainty considered together with the primitive probability law constraints, the reliability bound computations essentially require solving a pair of multi-linear optimization problems, which in general are non-convex and non-concave and therefore belong to a class of difficult optimization problems. Therefore, we develop a linear programming‐based cut-generation approach for solving the reliability bound assessment problem which achieves a computationally attractive approximation. Finally, the effectiveness of our approaches is validated in the case study with the comparisons to the published results.

KEYWORDS:

• Multi-state system (MSS)
• reliability assessment
• hybrid uncertainty
• judgemental estimate
• optimization

Acknowledgement

The authors would like to thank the anonymous referees for their constructive comments.

Funding

This work was partially supported by the National Natural Science Foundation of China under a key project grant No. 71731008.

Additional information

Notes on contributors

Shuming Wang

Shuming Wang received B.Sc. and M.Sc. degrees in applied mathematics from Hebei University, China in 2004 and 2007, respectively, and received his Ph.D. in engineering at Waseda University, Japan, 2011. He was a Special Research Fellow of the Japan Society for the Promotion of Science (JSPS), Japan (2009-2011), worked as a Researcher in Research Institute and Risk Management Division of China Galaxy Securities Co. LTD (HQ), Beijing, China (2011-2012). He also worked as a Research Fellow of the National University of Singapore (NUS), Singapore (2012-2015). In March 2016, Dr. Wang joined the School of Economics & Management, University of Chinese Academy of Sciences (UCAS), Beijing, as an assistant professor. He was also an adjunct researcher of Waseda University, Japan (2011-2015). Dr. Wang’s research interests are optimization under uncertainty, imprecise probability theory, energy system planning, and risk assessment and management, and he has authored or coauthored 30 journal papers in those fields and published one research monograph. He has also served as a referee for several journals, including IEEE Trans. on Systems, Man & Cybernetics: Systems, IEEE Trans. on Cybernetics, IEEE Trans. on Industrial Electronics, IEEE Trans. on Engineering Management, Information Sciences, and Annals of Operations Research. He is currently an associate professor at the school of economics and management, University of Chinese Academy of Sciences.

Yan-Fu Li

Yan-Fu Li is currently a professor at the Department of Industrial Engineering (IE), Tsinghua University. He is the director of the Reliability & Risk Management Laboratory at Institute of Quality and Reliability in Tsinghua University. He obtained his B.Eng degree in software engineering from Wuhan University in 2005 and a Ph.D. in industrial engineering from the National University of Singapore in 2010. He was a faculty member at the Laboratory of Industrial Engineering at CentraleSupélec, France, from 2011 to 2016. His current research areas include RAMS² (reliability, availability, maintainability, safety and security) assessment and optimization with the applications onto energy systems, transportation systems, computing systems, etc. He is the Principal Investigator on several government projects including one key project funded by National Natural Science Foundation of China, one project in National Key R&D Program of China, and the projects supported by EU and French funding bodies. He is also experienced in industrial research: partners include EDF, ALSTOM, China Southern Grid, etc. Dr. Li has published more than 90 research papers, including more than 40 peer-reviewed international journal papers. Dr. Li is currently an associate editor of IEEE Transactions on Reliability, a senior member of IEEE and a member of INFORMS. He is a member of the Executive Committee of the Reliability Chapter of Chinese Operations Research Society; Executive Committee of Industrial Engineering Chapter of Chinese Society of Optimization, Overall Planning and Economic Mathematics; Committee of Uncertainty Chapter of Chinese Artificial Intelligence Society.

Yakun Wang

Yakun Wang is currently a final year undergraduate student in the Department of Industrial Engineering at Tsinghua University. Her research mainly focuses on mixed integer programming with applications on railway maintenance scheduling.